SOFTENING BEHAVIOUR OF CONCRETE UNDER UNIAXIAL COMPRESSION

Transcription

1 Fracture Mechanics of Concrete Structures, Proceedings FRAMCOS-2, edited by Folker H. Wittmann, AEDIFICA TIO Publishers, D Freiburg (1995) SOFTENING BEHAVIOUR OF CONCRETE UNDER UNIAXIAL COMPRESSION M.R.A. van Vliet and J.G.M. van Mier Stevin Laboratory, Delft University of Technology Delft, The Netherlands Abstract The softening behaviour of concrete as found in laboratory tests depends strongly on structural aspects such as specimen dimensions, boundary conditions, feed-back signal and testing machine characteristics as well as on the concrete composition. In order to investigate these effects, the RILEM Committee 148ssc proposed a round robin test. The main goal of the round robin is to obtain a definition of a test-method for compressive strain softening behaviour. To contribute to this round robin, uniaxial compression tests have been performed in the Stevin Laboratory on concrete prisms with a constant cross section of 1OOx100 mm 2 Specimens with heights of 25, 50, 100 and 200 mm made of concrete qualities with compressive cube strengths of 50 MPa and 80 MPa, were loaded under two different restraining conditions. The tests were deformation controlled using the average vertical displacement of four LVDTs at the corners of the specimen as feed-back signal. Additionally the lateral deformations were measured by three horizontal LVDTs placed on each specimen side. One of the most important results of the tests is the reduction of the frictional stresses between concrete specimen and steel loading platen, by using an intermediate layer of teflon sheets and grease. When comparing these test results to those which specimen and loading platen were in direct contact, the influence of the specimen height on the compressive strength is found to disappear. 383

2 '-'!J",..,' '"' ''......,..,... AA...,AJ-,AA~, as small specimens occur. The effect the schematically in Fig. decreasing h/b 8 = 8/h (b) 1. boundary restraint (b) on the of concrete (Van to regard specimen as a use of displacements stead of strains. When Mier the of 384

3 the specimen height to disappear, resulting in curves that were almost on top of each other. Later Vonk (1992) continued the investigation of the concrete behaviour under uniaxial compression, mainly focussing on the influence of different friction reducing interlayers. Moreover, numerous numerical simulations of concrete softening under compression were carried out. Next to a second kind of steel brushes, consisting of longer brush rods, he also used a sheet of teflon as intermediate layer. The tests in which the boundary restraint was actively reduced were compared with tests in which so called "dry platens" were used. These "dry platens" consisted of polished and hardened steel platens that were in direct contact with the ground concrete surface. These test results confirmed the earlier findings ofkotsovos (1983). The influence of increasing frictional stresses between specimen and loading platen is shown schematically in Fig. 1 b. In order to get a complete overview of the influence of the parameters mentioned above on the softening behaviour of concrete, as well as the influence of measuring and control devices, testing machine parameters and concrete quality, RILEM Comittee l 48ssc was founded. As part of the round robin proposed by Comittee 148ssc, the compression tests described this paper have been performed. After describing the test set-up, the results are presented followed by a discussion that focusses on the influence of specimen size, boundary conditions and concrete quality. 2 Outline of experiments Test set-up For the tests described in this paper, prisms with a constant cross section of looxloo mm 2 and heights of 25, 50, 100 and 200 mm were used. The tests were carried out on a uniaxial compression machine with a capacity of 3000 kn. The machine is controlled by a closed loop servo hydraulic system. Of the two loading platens the lower one is fixed as the upper loading platen is connected to the machine by a hinge. this way the upper platen can adjust to geometrical imperfections of the test specimen. After the load has increased to some extent, the upper loading platen is automatically fixed and keeps this same position during the rest of the test. As one of the requirements of the round robin was a loading platen size matching the size of the specimen, an extra set of loading platens has been made. These hardened polished steel platens the same cross section as the concrete specimens and a height of 75 mm All compression tests each specimen except those twelve horizontal a JLAJL at... a.jljl.u.._..a

4 62.5 mm. on two mm below respective! y. placed on each axial deformations were measured of which the return was used as a feed-back signal to control the tests. deformation rate was 1 µmis. deformations, three LVDTs were placed the middle of the specimen and the other top end and 10 mm above the specimen bottom end specimens with a height of 25 mm, only one middle of the specimen. The horizontal '-'... _._... _._..._ range of ± 2 mm....,v..,_,..,,.,_,,,_..,._,_...,, prisms with dimensions of 150x150x600 six subsequent weeks. Three batches were...,,,,jl,l.....,.,ji...,... concrete (NSC), the other three were of high strength concrete (HSC). 1 mixtures are given that were used to obtain concrete qualities. and nine control cubes with dimensions were cast. At an age of 2 days prisms and cubes were a water basin. 14 days after casting the prisms specimens with heights of 25, 50, 100 and 200 mm back water basin. Within the next week all specimen parallel, in order to get a good contact between and to facilitate the adjustment of the trans- 386

5 ducers on to the specimens. At an age of 28 days the specimens were out of the water, and put in a plastic bag that was sealed afterwards. same time, six control cubes were taken out of the water basin determine the cube compressive strength and the tensile splitting Tab le 1. Concrete mix properties Unit content kg/m 3 8-4* 4-2* 2-1* 1-0.5* * * PCB MS SP w/c NSC HSC *grain size in mm, PCB: Portland Cement B, MS: Microsilica, SP: Superplasticizer Test procedure was as follows. A specimen was taken from the plastic bag and surface dried, such that the measuring device could be attached. a few more hours the specimen was tested. 2.3 Boundary conditions of the tests has been performed putting specimen and loading IUJLIUl....,.. Jl direct contact with each other. When using loading platens of JlH..11.Jl...,.,._...,... polished steel and ground concrete, considerable frictional stresses specimen and loading platen can develop. Therefore, addition to loading platens with High Friction (HF), loading platens reducing material between concrete and steel were used. This Jl...,...,LJ...,... Jl... ~..., layer was built up out of two teflon sheets with a thickness of 0.1 mm and a grease layer of mm in between. The latter type of loading.,. ~"-~.. will be referred to as Low Friction (LF) platens. 3 Experimental results section 2 the experimental set-up and the specimen preparation was discussed; in this section the main experimental results will be shown. a short explanation of the corrections that were made to the original test an overview of the different experiments is given by means of stress-strain curves. Comparing these stress-strain curves the effects of specimen boundary friction and concrete quality on the experimental results discussed. More detailed discussions will be given using the peak stresses, peak strains and normalized stress-strain curves. 3.1 Correction of data The data measured in the compression tests have been corrected different ways, both concerning the measurements of the four axial The first correction was made because of the strong increase of 387

6 test. This is due to adjustment of vv.. d.. L...,Jl. surface and the compressibility the tests. this behaviour makes the loadtests shift horizontally, an objective comparison...,... Jl.'U J.JL values become impossible. For this reason the of the load-deformation curves is replaced by a straight line, which was..,...,.....,...,... JI.... the pre-peak slope of the force-displacement...,,...,... From this point a line is drawn intersection point the x-axis. the curve is shifted until the intersection point is situated the origin. second correction was necessary because of the way in which the...,,...,..._,...,,.""'...,,.,..... llj...,,,,... u... was adjusted. As mentioned before the gauge length is JL.Jsr)ecumen + mm. that the measured axial deformations also..,,...,...'-4,uul the deformation of 62.5 mm of steel loading platens. Therefore deformations have corrected by the elastic deformation the It is mentioned that the curves shown this paper have order to eliminate noises from the experimental data. an overview stress-axial strain curves is given for the which the specimen height, the boundary conditions and the are varied. As each kind of experiment has been performed times, one that can be regarded as representative for that kind of 0 v 1 "'' -r""m 0 nt- is.,.~,.ll~~- For a overview the test results, see Van Vliet (1995). First the influences of specimen height and boundary restraint on the test results be discussed for NSC. Comparing the curves of the NSC different heights and loaded under HF boundary conditions, ""IJ""'""'...,...,... height strongly influences the peak load, see comparing 25 mm to the 200 mm specimens, the peak can increase up to 250%. This increase of peak load, is due to the effect the boundary restraint which is present almost the whole specimens of 25 mm and 50 mm height. The boundary restraint is caused by the frictional stresses specimen loading platens (Fig. 4). As a result,... JL...,JLJl...,......,...,,stresses between aggregates and voids causing failure concrete Mier, 1984), are only reached at substantially higher loads. the 100 mm and the 200 mm specimens, larger parts of the specimen are not affected by the frictional stresses. Failure will consequently occur in parts at lower loads. In contrast to the considerable difference stresses for the tests HF boundaries, the stresses were the boundary tests shows the eff ectivity of the interlayer, at least as peak stress is concerned. When ductility is defined as the slope of the post-peak stress vs. axial curve, ductility NSC tests (Fig. 3b) is lower compared 388

7 stress (MPa) stress (MPa) high friction low friction h=25 mm O--'-~~...-~~..--~~,..--~---; (a) strain (%0) strain (%0) stress (MPa) stress (MPa) high strength concrete high friction high low friction concrete h=25 mm h=25 mm o_...~~---~~...-~~..--~---1 Fig. 3. o_..._~_.:;;;...-~~,...~~,.--~ strain (%0) (c) (d) Stress vs. axial strain for the NSC (a,b) and HSC (a,c) and LF boundary conditions strain (%0) tested to the ductility of the HF NSC tests (Fig. 3a). found for the LF NSC tests, can be explained by growth for the LF and HF boundary conditions. cracks are free to choose the weakest path (see Fig. 5b ), which will yield a minimal release parts of the specimen are confined by frictional L'.._,...,.. HF tests, less cracks will develop here (Fig. 5a). of the specimen that is not influenced by boundary restraint, depends on the specimen height as shown in (Fig. 4). cracks are forced to grow in parts of the specimen that are not confined. Therefore, for conditions this will result in a higher release of elastic energy, compared to a situation without restrictions to crack growth. This restricted crack can also be seen when inspecting the crack surface of a specimen: it is smoother and shows more splitted aggregate particles of a LF specimen. The differences in crack growth between the ditions are also found the load-displacement response. 389

8 ac i i ~ 't i i i i i i i i i 't ac t t t t t t t t t t t t 4. Confined zones for different specimen heights due to boundary friction and lateral deformations of the 100 mm NSC specimens of 5 are plotted in Fig. 6. axial deformations are measured by the separate whereas the lateral deformations are the average of the deformations measured by the four in a horizontal plane. When LF boundaries are used, localization of deformations and thus......,..,,... crack growth takes place after peak load. Owing to this non ~ii~l~a,ua crack growth and despite the (supposed) non-rotatability of the loading platens, there can be substantial differences in stiffness over the specimen width. This causes differences in axial deformations (Fig. 6a). For tests, fracturing seems to occur more distributed through the specimen's The spalling of specimen's outer layers is more restrained in case, thereby forcing constant stress-redistributions (Fig. 6b ). main influences of the specimen height and the boundary restraint have been discussed using the results of the NSC specimens. When comparing the upper and the lower graphs of Fig. 3 it can be concluded that shows the same softening behaviour as the NSC, both under HF LF boundary conditions. The main difference between the two concrete qualities is the ductility, that is consistently higher in case of the NSC specimens. This higher ductility of the NSC can be explained by a front bottom (b) front bottom Crack patterns for 100 mm NSC specimen loaded under HF (a) and LF boundary conditions (b) 390

9 .-~~~~~~~~~_ 50 _~st_re_s_s_(m_p_a_)~~~~~~~- 40 low friction average signal -- separate LVDT's (a) specimen middle -- specimen ends lateral deformation (µm) axial deformation (µm) (b) specimen middle -- specimen ends lateral deformation (µm) average signal -- separate LVDT's axial deformation (µm) Fig. 6. Axial and lateral deformations of 100 mm NSC specimen (a) and HF boundary conditions (b) contemplation of the crack processes in concrete. When NSC is loaded, at first microcracks will develop in the bond zones between matrix and aggregates between about 30% and 70% of peak load. The first reason for cracks to start growing there, is the strength difference between the and both matrix and grains. Secondly, stress-concentrations will develop around the interface between the stiff aggregates and the matrix, owing to their difference in Young's modulus. In HSC, the differences strength and stiffness ratios are equalized, leading to a more homogeneous structure. As a consequence, crack arrest by stiff er aggregate particles is not possible anymore making the first cracks more critical. Another factor might be the porosity of the matrix and bond zones in NSC, again leads to stress concentrations. In HSC this effect will also be substantially less. The aforementioned mechanisms make HSC specimens more brittle. This brittle failure made it impossible to control the 200 mm experiments by means of the average vertical deformation. Using (average) lateral deformation as a control signal, will solve this problem. 391

10 ..., JL" concerns the tail of the stress-strain curve of the 25 mm (Fig. 3b,d). After reaching a lowest point, the course, a height of 25 mm is rather extreme compared to U... Jl... aggregate 8 mm, but also the 50 mm specimens show at the end the tail. For higher specimens It is however most likely that eventually all of behaviour, be it at later stages the applied load be explained by is created between loading platens, distance when specimens with a height over AAA._... are tested. the moment the specimen has is solely carried by the aggregate particles and CJ...,,.,...,... even peak will be reached. pointed out of be it that ""'n' ""r"rn'"'"r'" of increasing deformational resistance was experiment'. stress-strain curves are in Fig. 7, all performed. The peak stresses and strains for HF and boundary conditions are plotted...,...'"'... of the slenderness. The stress values are given in Table sheets grease as an anti-friction layer between specimen is effective, as can be seen Fig. The peak..,.,.,...,...,,u..."" independent of the specimen height, and the scatter in decreased considerably. values of the ultimate strengths ijjlj.jl...,... specimens are equal to those of the 200 mm specimens. It can the specimens tested under LF boundary conditions no anymore. Peak stresses of the NSC and the HSC experiments a peak (MPa) for NSC apeak (MPa) for HSC LF HF ~~ LF HF ~~ 36.0± ± ± ± ± ± ± ± ±1.l 84.9± ± ± ± ± ± ± ± ±1.6 * Compressive strength of 150 mm control cubes levelling the platens according to the peak scatter becomes smaller both the peak stresses and peak test results (Fig. 8). The decreasing scatter of for increasing specimen height. Especially in 392

11 peak stress (MPa) high friction low friction peak stress (MPa) high strength concrete g 0 high friction low friction Q 50 I 50 o---~--~... ~~...-~-...-~-- o_,_~-.-~---.~~...-~-..-~-- o 0.5 i.0 i o (a) slenderness (h/w) 16 strain at peak stress (%0) strain at peak stress (%0) 16 O high friction slenderness high strength concrete O high friction 12 0 low friction 12 0 low friction slenderness (h/w) slenderness (c) 7. Peak stresses (a,b) and strains (c,d) for NSC (a,c) HSC (d) case of tests the scatter peak stresses peak strains becomes smaller with increasing specimen height. For the tests, the large ence in standard deviation for the peak stresses is due to boundary influences on the stress distribution inside a substantial discontinuity the concrete, the be bigger a small specimen than for a large one, as the latter case the influence is averaged over a larger area. Such discontinuities might also reason decrease of the peak stress that is found for slenderness values than 1, see Fig. 7. scatter in the peak strains found the HF tests is loading platens. These influence the strain distribution specimen as as the real deformations of the loading platens the contact area between loading platen and specimen. Although the measured deformations have been corrected for the computed elastic deformation of steel platens, the real deformations of loading platens contact area are not known. As this effect is still included in the deformation values to compute the peak strains, the scatter be more pronounced for 25 mm specimens than for the 200 mm ones. Apart from this effect 393

12 distribution the specimen near the loading platens is far from constant. unfortunately not be distinguished from the and contact area that was mentioned first. stress (MPa) stress (MPa) low friction h=25 mm 200 O+-~~...-~... ~~-...~~-l strain (%0) strain (%0) (a) Fig. 8. Range of results NSC specimens HF and boundaries... uuu,..,...,,,...,..., of the specimen height on values for peak stress and the peak strain strongly decreases for the specimens with a length of 100 mm or more. the 100 mm specimens peak stresses are close to those the 150 mm control cubes (they are about 5 MPa lower). Differences are however likely to occur as specimens have been ground contrast to the control cubes. frictional stresses that will develop between the ground surface of the specimen and the steel loading platens will therefore be lower compared to the control cubes, resulting in a lower peak stress. Moreover, the 150 mm control cubes were loaded immediately after they were removed from the water. contrast, the ( 100 mm) specimens were loaded only after 6-8 hours of removal from the plastic bags. Consequently eigenstresses will develop, causing a lower apparent tensile strength. Normalized curves Normalized stress-strain curves can be used to provide insight into the specific differences in the behaviour of specimens of varying heights under different loading conditions. By dividing the stresses and strains by the stress strain values at the peak, a comparison can be made of the pre-peak and the post-peak specimen behaviour. In Fig. 9 the normalized stress-strain curves for the NSC tests are shown. With regard to the HF tests, the non-linearity of the pre-peak curve increases decreasing specimen height, see Fig. 9a. Although the ences curve shape are not too large for specimens with heights of 50 mm, 100 mm and 200 mm, for a specimen height of 25 mm a gradual decrease of the slope is found for forces larger than 60% of peak load. The curves of the tests however, do not show this behaviour which confirms the difference 394

13 crack growth due to HF or LF boundary conditions. Decrease of the prepeak slope is caused by the development of mortar cracks, coalescence of cracks and premature spalling of specimens outerlayers. For the specimens and the specimens higher than 100 mm processes start between 80% and 90% of the peak load. At lower loads cracks originate in the bond zones between mortar and aggregate. formation microcracks however, is hardly possible in the 50 mm, especially the 25 mm specimens tested under HF boundary conditions. Owing to the.,h~~aa~ ary restraint in case of the HF boundary conditions, these specimens are almost totally confined in horizontal direction, allowing less micro-cracks to develop. As a result the process of mortar crack development, coalescence of cracks and macro crack formation will already start at lower load levels causing a decrease of the slope of the stress-strain curve high friction.o normalized stress low friction O+-~-...~--...~~...-~...,.-~--; normalized strain (a) ~-..-~--.-~~...-~...,.-~ normalized strain (b) Fig. 9. Normalized stress-strain curves for the The post-peak parts of the normalized curves shown in 9, once again emphasize the influence of the specimen height on the softening behaviour of concrete. The influence of the specimen height on the softening behaviour of concrete is as strong for the HF as for the LF boundary conditions, increases with decreasing specimen height. Consequently, testing specimens with a too low slenderness without active reduction of boundary friction, gives a too high tail of the softening curve of concrete. In general one can say the ductility decreases considerably with increasing specimen height. Kotsovos ( 1983) stated when observing this behaviour that, if the friction reduction in the boundaries would be perfect, in the most extreme case the post-peak slope of the curve would be vertical. Therefore he suggested taking the post-peak strength of concrete under compression equal to zero. This seems too radical however. Although the load decreases rapidly for the 200 mm specimens, it does not become zero and a clearly present. Furthermore, it is not unlikely his results were affected by snap-back behaviour, which would make his conclusions rather debatable. 395

14 4 Conclusions Uniaxial compression tests on prisms of two different concretes, with different heights and under low and high frictional restraint, have shown that a stress-strain curve of concrete is not a material property but a mix of structural and material behaviour. By applying an interlayer of teflon and grease between specimen and loading platen the effect of the specimen height on the peak stresses and peak strains could be effectively reduced. The elastic energy release however, is still influenced by the specimen height for both the 50 MPa and the 80 MPa concrete. The difference between the two types of concrete is the release of elastic energy that is lower for the 80 MPa concrete. The effect of the specimen height on localized fracture modes is subject of further study. Acknowledgements The authors are greatly indebted to Mr. A.S. Elgersma for his assistance in building the experimental set-up and carrying out the experiments presented in this paper. The work was sponsored through a grant from the Dutch Technology Foundation (STW). References Armer, G.S.T. and Grimer, (1989) On the use of full stress-strain characteristics in structural analysis. Mat. and Struct., , Kotsovos, M. D. (1983) Effect of testing techniques on the post-ultimate behaviour of concrete compression. Mat. and Struct., 16-91, Van Mier, J.G.M. (1984) Strain-Softening of Concrete under Multiaxial Loading Conditions. PhD Thesis, Eindhoven University of Technology, The Netherlands. Van Vliet, M.R.A. and Van Mier, J.G.M. (1994) Comparison oflattice type fracture models for concrete under biaxial loading regimes, in Proc. IUTAM Symp. on Size-Scale Effects in the Failure Mechanisms of Materials and Structures (in press), Oct. 3-7, Torino, Italy. Van Vliet, M.R.A. and Van Mier, J.G.M. (1995) Strain-softening behaviour of concrete in uniaxial compression. Report , Delft University of Technology, The Netherlands. Vonk, R. ( 1992) Softening of Concrete loaded in Compression. PhD Thesis, Eindhoven University of Technology, The Netherlands. 396